We develop and estimate a microeconometric model of household labour supply in four European countries representative of different economies and welfare policy regimes: Denmark, Italy, Portugal and the United Kingdom. We then simulate, under the constraint of constant total net tax revenue (fiscal neutrality), the effects of various hypothetical tax-transfer reforms which include alternative versions of a Basic Income policy: Guaranteed Minimum Income, Work Fare, Participation Basic Income and Universal Basic Income. We produce indexes and criteria according to which the reforms can be ranked and compared to the current tax-transfer systems. The exercise can be considered as one of empirical optimal taxation, where the optimization problem is solved computationally rather than analytically. It turns out that many versions of the Basic Income policies would be superior to the current system. The most successful policies are those involving non means-tested versions of basic income (Universal or Participation Basic Income) and adopting progressive tax-rules. If - besides the fiscal neutrality constraint - also other constraints are considered, such as the implied top marginal top tax rate or the effect on female labour supply, the picture changes: unconditional policies remain optimal and feasible in Denmark and the UK; instead in Italy and Portugal universal policies appear to be too costly in terms of implied top marginal tax rates and in terms of adverse effects on female participation, and conditional policies such as Work-Fare, emerge as more desirable.